Aster repulsion drives local ordering in an active system

Biological systems are a form of active matter, which often undergo rapid changes in their material state, e.g. liquid to solid transitions. Yet, such systems often also display remarkably ordered structures. It remains an open question as to how local ordering occurs within active systems. Here, we utilise the rapid early development of Drosophila melanogaster embryos to uncover the mechanisms driving short-ranged order. During syncytial stage, nuclei synchronously divide (within a single cell defined by the ellipsoidal eggshell) for nine cycles after which most of the nuclei reach the cell cortex. Despite the rapid nuclear division and repositioning, the spatial pattern of nuclei at the cortex is highly regular. Such precision is important for subsequent cellularisation and morphological transformations. We utilise ex vivo explants and mutant embryos to reveal that microtubule asters ensure the regular distribution and maintenance of nuclear positions in the embryo. For large networks of nuclei, such as in the embryo, we predict - and experimentally verify - the formation of force chains. The ex vivo extracts enabled us to deduce the force potential between single asters. We use this to predict how the nuclear division axis orientation in small ex vivo systems depend on aster number. Finally, we demonstrate that, upon nucleus removal from the cortex, microtubule force potentials can reorient subsequent nuclear divisions to minimise the size of pattern defects. Overall, we show that short-ranged microtubule-mediated repulsive interactions between asters can drive ordering within an active system.